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EXAMPLE 4 Find f if f′′(x)=12x2+6x−4,f(0)=8, and f(1)=5. SOLUTION The general antiderivative of f′′(x)=12x2+6x−4 is f′(x
Posted: Thu Jul 14, 2022 4:36 pm
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- Example 4 Find F If F X 12x2 6x 4 F 0 8 And F 1 5 Solution The General Antiderivative Of F X 12x2 6x 4 Is F X 1 (34.69 KiB) Viewed 33 times
EXAMPLE 4 Find f if f′′(x)=12x2+6x−4,f(0)=8, and f(1)=5. SOLUTION The general antiderivative of f′′(x)=12x2+6x−4 is f′(x)=12x−6+Cx−4x+C= Using the antidifferentiation rules once more, we find that f(x)=4+x+3x+Cx+D=Cx+D. To determine C and D we use the given conditions that f(0)=8 and f(1)=5. Since f(0)=0+D=8, we have D=. Since f(1)=1+1−2+C+=5 we have C=. Therefore, the required function is f(x)=